Hybrid Inverse Design Method for Nonlifting Bodies in Incompressible Flow

Abstract

A methodology for the inverse design of nonlifting axisymmetric and nonaxisymmetric bodies in incompressible flow is presented. In this method, an inverse design approach based on conformal mapping is used to design a set of airfoils in isolation. These airfoils are then assembled into a three-dimensional body and the flow over the body is calculated using a panel method. The inverse design parameters for the isolated airfoils are adjusted by a multidimensional nonlinear solver to achieve the desired aerodynamic properties on the three-dimensional body. The method can be used with fairly complex geometries, such as bodies in the presence of a wing or keel. The suitability and performance of several numerical schemes are compared in the paper. Several examples are presented that demonstrate the flexibility of the design method when applied to various representative design problems and they also show the ability of the method to match a known velocity distribution. Nomenclature A = area B = approximate Jacobian c = chord length c i = control airfoil F = vector of functional relations f i = functional relations to be zeroed h = surface displacement J = Jacobian matrix _ m = mass-flux n = dimension of nonlinear system n = surface normal Re = Reynolds number s = arc length s i = control sectioñ s = arc length relative to beginning of section u = normal velocity u t = transpiration velocity V 1 = freestream velocity _ v = volume flux v i = relative velocity along a splined segment x i = unknown variables x = vector of unknown variables x = correction vector = angle of attack, deg = segment design angle of attack = arc limit = arc limit relative to beginning of segment = source strength V = velocity difference over a segment normalized by the freestream velocity Subscripts i = segment number on an airfoil or the equivalent segment of the body cross-section p = unperturbed surface panel t = transpiration